Dominic Welsh is a leading contributor to combinatorial mathematics in several ways. In research, his significant contributions began with his doctoral thesis, "On stochastic processes, with special reference to percolation theory". This was a basis for much further work, including the Russo-Seymour-Welsh theorem. He has made significant contributions to matroid theory, including a text with that title, which held centre stage in that discipline for fifteen years, until the spotlight shifted to a text by one of his former research students - James Oxley. Another significant paper describes how unavoidably complex it is to calculate Tutte polynomials for graphs, and Jones polynomials for knots. These are samples: in all, there are over eighty research articles, seven textbooks, thirty research students.